What is inverse oflaplace ((3s+16))/(s^2-16) ?

The answer to inverse oflaplace ((3s+16))/(s^2-16) is -1/2 e^{-4t}+7/2 e^{4t}

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inverse oflaplace ((3s+16))/(s^2-16)

inverse laplace

\frac{( 3 s + 16 )}{s ^{2} - 16}

- \frac{1}{2} e^{- 4 t} + \frac{7}{2} e^{4 t}

Solution steps

L^{- 1} {\frac{( 3 s + 16 )}{s ^{2} - 16}}

Take the partial fraction of

\frac{3 s + 16}{s ^{2} - 16} : - \frac{1}{2 ( s + 4 )} + \frac{7}{2 ( s - 4 )}

= L^{- 1} {- \frac{1}{2 ( s + 4 )} + \frac{7}{2 ( s - 4 )}}

Use the linearity property of Inverse Laplace Transform:

For functions

f (s), g (s)

and constants

a, b : L^{- 1} {a \cdot f (s) + b \cdot g (s)} = a \cdot L^{- 1} {f (s)} + b \cdot L^{- 1} {g (s)}

= - L^{- 1} {\frac{1}{2 ( s + 4 )}} + L^{- 1} {\frac{7}{2 ( s - 4 )}}

L^{- 1} {\frac{1}{2 ( s + 4 )}} : \frac{1}{2} e^{- 4 t}

L^{- 1} {\frac{7}{2 ( s - 4 )}} : \frac{7}{2} e^{4 t}

= - \frac{1}{2} e^{- 4 t} + \frac{7}{2} e^{4 t}

x \to 2 lim (3 ∣ x - 2 ∣)

x \to 7 lim (\frac{x ^{2} + 7}{x})

\int \frac{3 x - 13}{x ^{2} + 3 x - 10} d x

(5 x^{3} + 3) (x^{4} - 2 x)

\int \frac{1}{( 4 x ^{2} + 1 ) ^{2}} d x

What is inverse oflaplace ((3s+16))/(s^2-16) ?
The answer to inverse oflaplace ((3s+16))/(s^2-16) is -1/2 e^{-4t}+7/2 e^{4t}